Question: The function $f(x)$ satisfies
\[f(x + y) = f(x) f(y)\]for all real numbers $x$ and $y.$  If $f(2) = 3,$ find $f(6).$
Taking $x = 2$ and $y = 2,$ we get
\[f(4) = f(2) f(2) = 9.\]Taking $x = 4$ and $y = 2,$ we get
\[f(6) = f(4) f(2) = \boxed{27}.\]